Characterization and Mathematical Modelling of Geometric Effects on Piezoelectric Actuators

2019 ◽  
Vol 201 (1) ◽  
pp. 201-217
Author(s):  
Hareem Jawaid ◽  
Waqar Ahmed Qureshi ◽  
Riffat Asim Pasha ◽  
Rizwan Ahmed Malik
Keyword(s):  
Mathematical Model ◽  
Structural Analysis ◽  
Mathematical Modelling ◽  
Piezoelectric Actuator ◽  
Piezoelectric Actuators ◽  
Numerical Results ◽  
Hydraulic Valves ◽  
Geometric Effects

This paper focuses on the characterization and static structural analysis of piezoelectric actuator to investigate the sequential increasing effect of piezoelectric patches. The effect on the tip deflection is observed analytically, numerically and experimentally. By varying the quantity and the geometry of piezoelectric patches/beams, the actuation effect is analyzed. A mathematical model has been developed for the unequal lengths of patches and beam. The analysis is carried out numerically to examine the tip deflection under various parameters. The results are analyzed and verified experimentally. The results are found to be in accordance with the analytical and numerical results. This permits the desired configuration of an actuator in applications like hydraulic valves for actuating and controlling the flow of liquid as per need.

Mathematical Modelling the Process of Cup Wheel Precision Grinding of Rotating Concave Paraboloid

2016 ◽  
Vol 693 ◽  
pp. 837-842
Author(s):  
Fu Yi Xia ◽  
Li Ming Xu ◽  
De Jin Hu
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Abrasive Particle ◽  
Influence Factors ◽  
Machining Process ◽  
Quadric Surface ◽  
Precision Grinding ◽  
Cup Wheel ◽  
The Mathematical Model ◽  
Trajectory Equation

A novel principle of cup wheel grinding of rotating concave quadric surface was proposed. The mathematical model of machining process was established to prove the feasibility of precision grinding of rotating concave paraboloid based on the introduced principle. The conditions of non-interference grinding of concave paraboloid were mathematically derived. The processing range and its influence factors were discussed. The trajectory equation of abrasive particle was concluded. Finally, the math expressions of numerical controlled parameters was put forward in the process of grinding of the concave paraboloid.

Compact Drive Electronics for Solid-State Actuators

2000 ◽  
Author(s):  
Jeffrey S. N. Paine ◽  
David S. Bennett ◽  
Carlos E. Cuadros
Keyword(s):  
Solid State ◽  
Power Electronics ◽  
Piezoelectric Material ◽  
Piezoelectric Actuator ◽  
Power Dissipation ◽  
Piezoelectric Materials ◽  
Piezoelectric Actuators ◽  
Linear Amplifier ◽  
Overall Efficiency ◽  
Electronics Packages

Abstract As piezoelectric actuators are developed for high strokes and/or high force applications, the amount of piezoelectric material used in the actuator must also increase. Reducing the size of drive electronics becomes difficult using traditional linear power electronics packages when applications require as much as 40 μF of piezoelectric load. In order to efficiently drive piezoelectric actuator systems, bi-directional systems (drivers that recover the energy put into the piezoelectric capacitor) must be used. Since less than 10% of the power going into the piezoelectric actuator is real versus the large reactive load used to power the piezoelectric materials, bidirectional systems have a much higher efficiency. A comparison is made between traditional linear and PWM amplifier systems and tailored piezoelectric bi-directional driver systems. Bi-directional systems have power dissipation levels up to 1/8th those of traditional linear amplifier systems. In the course of the research both linear and PWM concepts were investigated. A rationale for comparing the overall efficiency of drive electronics systems is presented. Some innovative efficient concepts for piezoelectric system drivers are presented and discussed.

Mathematical modelling.

2021 ◽  
Author(s):  
Ed Rutgers Durner
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Mathematical Models ◽  
Growth And Development ◽  
Fertilizer Recommendations ◽  
Mathematical Equations

Abstract Plants are studied to understand their growth and development so that their quality and productivity can be optimised. Models are developed that can be simple and descriptive, or quite complex with numerous mathematical equations; their level of complexity is linked to their purpose. This summary serves as an introduction to mathematical models in horticulture. It is not a manual for modelling itself, but rather an overview of how important mathematical models are in horticultural production. Mathematical models are used extensively in horticulture both extrinsically, i.e. when calculating chilling hour accumulations and intrinsically, i.e. when applying fertilizer to a crop. In chilling calculations, developed models are used directly. Fertilizer recommendations were probably developed using a mathematical model. The first part of this article discusses models in general and reviews general characteristics of mathematical models. The second part outlines the major uses of mathematical modelling in modern horticultural production. Presentations of specific models are limited in order to present a general discussion of models with examples that will interest most horticulturists.

scholarly journals Modelling Macrophage Infiltration into Avascular Tumours

2002 ◽  
Vol 4 (1) ◽  
pp. 21-38 ◽  
Author(s):  
C. E. Kelly ◽  
R. D. Leek ◽  
H. M. Byrne ◽  
S. M. Cox ◽  
A. L. Harris ◽  
...  
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Spatial Structure ◽  
Random Motion ◽  
Numerical Results ◽  
Macrophage Infiltration ◽  
Numerical Techniques ◽  
Model Predictions ◽  
Independent Experimental Data

In this paper a mathematical model that describes macrophage infiltration into avascular tumours is presented. The qualitative accuracy of the model is assessed by comparing numerical results with independent experimental data that describe the infiltration of macrophages into two types of spheroids: chemoattractant-producing (hepa-1) and chemoattractant-deficient (or C4) spheroids. A combination of analytical and numerical techniques are used to show how the infiltration pattern depends on the motility mechanisms involved (i.e. random motion and chemotaxis) and to explain the observed differences in macrophage infiltration into the hepa-1 and C4 spheroids. Model predictions are generated to show how the spheroid's size and spatial structure and the ability of its constituent cells influence macrophage infiltration. For example, chemoattractant-producing spheroids are shown to recruit larger numbers of macrophages than chemoattractant-deficient spheroids of the same size and spatial structure. The biological implications of these results are also discussed briefly.

scholarly journals MATHEMATICAL MODELLING OF THE UNMANNED AERIAL VEHICLE DYNAMICS

2018 ◽  
pp. 37-44
Author(s):  
V. Y. Stepanov
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Unmanned Aerial Vehicle ◽  
Vehicle Dynamics ◽  
Point Of View ◽  
Dynamics Analysis ◽  
Aerial Vehicle ◽  
Main Components ◽  
Controlled Object

The article gives a classification of the main components of unmanned aerial vehicle (UAV) systems, gives the areas in which the application of UAVs is actual in practice today. Further, the UAV is considered in more detail from the point of view of its flight dynamics analysis, the equation necessary for creating a mathematical model, as well as the model of an ordinary dynamic system as a non-stationary nonlinear controlled object, is given. Next, a description of the developed software for modeling and a description of program algorithm are given. Finally, a conclusion describes the necessary directions for further scientific researches.

Mathematical Modelling the Power Supply-Load System for Electro-Discharge Polishing Process

2010 ◽  
Vol 159 ◽  
pp. 125-128
Author(s):  
A. Parshuta ◽  
V. Chitanov ◽  
Lilyana Kolaklieva ◽  
Roumen Kakanakov
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Numerical Solution ◽  
Power Supply ◽  
Equation System ◽  
Electrolyte Temperature ◽  
Polishing Process ◽  
The Real ◽  
Quadratic Interpolation ◽  
Runge Kutta

The real electro-discharge polishing (EDP) system has been presented by an equivalent electrical scheme and described by a corresponded equation system. The Runge-Kutta-Merson method with automatically changed step is used for the numerical solution the equation system. The current through the resistor equivalent to the steam gas wrapper is defined with an I-V characteristic obtained by the method of multi-interval quadratic interpolation-approximation. A mathematical model of the power supply-load system has been realized in Basic and Matlab® languages. On the base of the developed modelling conditions limiting the current and voltage overload in the EDP system have been determined depending on the maximum polished area and the electrolyte temperature.

scholarly journals Application of Linear and Nonlinear Graphs in Structural Synthesis of Kinematic Chains

1973 ◽  
Vol 95 (2) ◽  
pp. 525-532 ◽  
Author(s):  
M. Huang ◽  
A. H. Soni
Keyword(s):  
Mathematical Model ◽  
Graph Theory ◽  
Structural Analysis ◽  
Three Dimensional ◽  
Structural Synthesis ◽  
Kinematic Chains ◽  
Piston Cylinder ◽  
General Constraints ◽  
Analysis And Synthesis ◽  
Linear And Nonlinear

Using graph theory and Polya’s theory of counting, the present paper performs structural synthesis and analysis of planar and three-dimensional kinematic chains. The Section 2 of the paper develops a mathematical model that permits one to perform structural analysis and synthesis of planar kinematic chains with kinematic elements such as revolute pairs, cam pairs, springs, belt-pulley, piston-cylinder, and gears. The theory developed is applied to enumerate eight-link kinematic chains with these kinematic elements. The Section 3 of the paper develops a mathematical model that permits one to perform structural analysis and synthesis of multi-loop spatial kinematic chains with higher and lower kinematic pairs. The theory developed is applied to enumerate all possible two-loop kinematic chains with or without general constraints.

scholarly journals Quantification of plasma cell dynamics using mathematical modelling

2018 ◽  
Vol 5 (1) ◽  
pp. 170759 ◽  
Author(s):  
Marcel Mohr ◽  
Dirk Hose ◽  
Anja Seckinger ◽  
Anna Marciniak-Czochra
Keyword(s):  
Mathematical Model ◽  
Bone Marrow ◽  
Mathematical Modelling ◽  
Plasma Cells ◽  
Cell Dynamics ◽  
Growth And Survival ◽  
Specific Antibodies ◽  
Health And Disease ◽  
Potential Basis ◽  
The Impact

Plasma cells (PCs) are the main antibody-producing cells in humans. They are long-lived so that specific antibodies against either pathogens or vaccines are produced for decades. PC longevity is attributed to specific areas within the bone marrow micro-environment, the so-called ‘niche’, providing the cells with required growth and survival factors. With antigen encounters, e.g. infection or vaccination, new PCs are generated and home to the bone marrow where they compete with resident PCs for the niche. We propose a parametrized mathematical model describing healthy PC dynamics in the bone marrow. The model accounts for competition for the niche between newly produced PCs owing to vaccination and resident PCs. Mathematical analysis and numerical simulations of the model allow explanation of the recovery of PC homoeostasis after a vaccine-induced perturbation, and the fraction of vaccine-specific PCs inside the niche. The model enables quantification of the niche-related dynamics of PCs, i.e. the duration of PC transition into the niche and the impact of different rates for PC transitions into and out of the niche on the observed cell dynamics. Ultimately, it provides a potential basis for further investigations in health and disease.

Simulation of fuel bed ignition by wildland firebrands

2018 ◽  
Vol 27 (8) ◽  
pp. 550 ◽  
Author(s):  
O. V. Matvienko ◽  
D. P. Kasymov ◽  
A. I. Filkov ◽  
O. I. Daneyko ◽  
D. A. Gorbatov
Keyword(s):  
Mathematical Model ◽  
Pinus Sylvestris ◽  
Mathematical Modelling ◽  
Thermal Energy ◽  
Ignition Time ◽  
Pine Bark ◽  
Bark Sample ◽  
Airflow Velocity ◽  
Experimental Conditions ◽  
Series Of Experiments

A 3-D mathematical model of fuel bed (FB) ignition initiated by glowing firebrands originating during wildland fires is proposed. In order to test and verify the model, a series of experiments was conducted to determine the FB ignition time by a single pine bark and twig firebrand (Pinus sylvestris). Irrespective of the pine bark sample sizes and experimental conditions, the ignition of the FB was not observed. Conversely, pine twigs, under certain parameters, ignited the FB in the range of densities (60–105 kg m−3) and with the airflow velocity of ≥2 m s−1. The results of the mathematical modelling have shown that a single pine bark firebrand ≤5 cm long with a temperature of T ≤ 1073 K does not ignite in the flaming mode the FB, and only the thermal energy of larger particles is sufficient for flaming ignition of the adjacent layers of the FB. The analysis of the results has shown that the firebrand length is a major factor in the initiation of ignition. Comparison of the calculated and observed FB ignition times by a single firebrand have shown that our modelling accords well with the experimental results.

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